Can charge flow to a neutral body? If an electrically positive object is kept with a neutral object, in which direction will charge flow?  Will charge flow from positive to neutral until both have equal charges, or will nothing happen to the neutral charge?
 A: It sounds like you're asking "If two conductive materials are brought in contact, and one of them is electrically neutral, and one is positively charged, which direction will charge flow?"
If that is indeed your question, then the answer is that negative charges (electrons) will flow from the neutral object to the positive object until they are at the same electrical potential (both bodies will end up positively charged).
The reason is this: the positively charged object will exert an attractive force on each electron in the neutral object, and a repulsive force on each proton in the neutral object. However, the protons are unable to move, being bound to the nucleus, which is stuck in a lattice of chemical bonds. The electrons in the highest energy levels, on the other hand, are free to move in a conductor, so they react to the attractive force by flowing towards the positively charged object.
A: It all depends by what you mean by the word "flow".
Let the charged body which is assumed to be a conductor produce an E-field.

In a conductor which has mobile charge carriers then the charges can be made to flow within a conducting body which has no net charge.
If you subject an uncharged conducting body to an external E-field then the mobile charge carriers will move under the influence of that E-field.
In moving there will be a separation of charge within the body and that charge is called the induced charge.
That induced charge sets up its own E-field in opposition to the external E-field.
Assume that you have an uncharged insulator and subject it to external E-
Eventually the E-field set up by the induced charge is equal in magnitude to the external E-field and so the net E-field inside the conductor with no net charge is zero.
On touching the two bodies together some charge will flow from the charged body to the uncharged body until they are at the same potential.

For an insulator things are a little different in that an ideal insulator has no mobile charge carriers.
Under the influence of an external E-field the electron shells around the nuclei of the atoms/molecules which make up the insulator are distorted so that there is a separation of charge within the atoms/molecules.  This separation of charge is called an electric dipole and produces its own E-field again in opposition to the external E-field.  However unlike a conductor the induced dipoles in an insulator only succeed in reducing the net E-field through the insulator.
So in an insulator the “flow”/movement of charges is very limited.
If the bodies touch in this case no charge will flow as the insulator has no mobile charge carriers.
This answer is related to the question Why does the electric force depend on the medium.
